Determination of the Antiferroquadrupolar Order Parameters in UPd3

TL;DR

This study combines heat capacity and X-ray resonant scattering to identify the specific antiferroquadrupolar order parameters in UPd3, resolving longstanding uncertainties about its quadrupolar phases.

Contribution

It uniquely determines the order parameter of the high-temperature phase as antiphase Q_{zx} and clarifies the nature of lower temperature phases through azimuthal dependence analysis.

Findings

High-temperature phase has antiphase Q_{zx} order parameter.

Lower temperature phases are superpositions of order parameters.

Heat capacity features reveal the order of phase transitions.

Abstract

By combining accurate heat capacity and X-ray resonant scattering results we have resolved the long standing question regarding the nature of the quadrupolar ordered phases in UPd_3. The order parameter of the highest temperature quadrupolar phase has been uniquely determined to be antiphase Q_{zx} in contrast to the previous conjecture of Q_{x^2-y^2} . The azimuthal dependence of the X-ray scattering intensity from the quadrupolar superlattice reflections indicates that the lower temperature phases are described by a superposition of order parameters. The heat capacity features associated with each of the phase transitions characterize their order, which imposes restrictions on the matrix elements of the quadrupolar operators.